Use the graph of sin (θ) above to estimate the value of θ when sin (θ) = -0.6 for \(0^o ≤ θ ≤ 360^o\)
A.
θ = 223\(^o\), 305\(^o\)
B.
θ = 210\(^o\), 330\(^o\)
C.
θ = 185\(^o\), 345\(^o\)
D.
θ = 218\(^o\), 323\(^o\)
Correct answer is D
On the \(y\)-axis, each box is \(\frac{1 - 0}{5} = \frac{1}{5}\) = 0.2unit
On the \(x\)-axis, each box is \(\frac{90 - 0}{6} = \frac{90}{6} = 15^o\)
⇒ \(θ_1 = 180^o + (2.5\times15^o) = 180^o + 37.5^o = 217.5^o ≃ 218^o \)(2 and half boxes were counted to the right of 180\(^o\))
⇒ \(θ_2 = 270^o + (3.5\times15^o) = 270^o + 52.5^o = 322.5^o ≃ 323^o \)(3 and half boxes were counted to the right of 270\(^o\))
∴ \(θ = 218^o, 323^o\)
